Manifold Theory

An Introduction for Mathematical Physicists

D. Martin

• Publisher: Woodhead Publishing
• Year: 2002
• Print ISBN:
  9781898563846
• eBook ISBN:
  9780857099631
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject. - Provides a comprehensive account of basic manifold theory for post-graduate students - Introduces the basic theory of differential geometry to students in theoretical physics and mathematics - Contains more than 130 exercises, with helpful hints and solutions

Table of contents

• Front Cover
• Manifold Theory: Introduction for Mathematical Physicists
• Copyright Page
• Table of contents
• About our Author
• Dedication
• Preface
• Chapter 1. Vector spaces
• Chapter 2. Tensor algebra
• Chapter 3. Differentiable manifolds
• Chapter 4. Vector and tensor fields on a manifold
• Chapter 5. Exterior differential form
• Chapter 6. Differentiation on a manifold
• Chapter 7. Pseudo-Riemannian and Riemannian manifolds
• Chapter 8. Symplectic manifolds
• Chapter 9. Lie groups
• Chapter 10. Integration on a manifold
• Chapter 11. Fibre bundles
• Chapter 12. Complex linear algebra, almost complex manifolds
• Appendix 1: Analytic topology
• Appendix 2: Quaternions and Cayley numbers
• Appendix 3: The semidirect product of two groups
• Appendix 4: Homotopy review
• Bibliography
• Some answers, some hints and some fragmentary solutions to the exercises
• Index